10MT_Project_Diabetes_Analysis
Peng Yuan
2023-04-16
Analysis of Diabetes Factors
In this trial, the physical data of diabetic patients were used as a basis for predicting whether or not they had diabetes. The dataset contains the following data.
Pregnancies - Number of pregnancies (continuous variable) Glucose - Check out the glucose contained in the body (continuous variable) BloodPressure - Human blood pressure (continuous variable) SkinThickness - (continuous variable) Insulin - Insulin values in the body (continuous variable) BMI - (continuous variable) DiabetesPedigreeFunction - Provide a history of diabetes in relevant family members (continuous variable) Age - (continuous variable) Outcome - Whether sick or not (categorical variable)
This experiment will be divided into four parts. The first part is to perform a preliminary visual analysis of the data. The second part starts the modeling analysis of the different relationships of the variables. The third part is to compare and select the optimal model and perform prediction. the fourth part train/tune with resampling.
Part 0: Loading packages and data
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library(splines)
library(yardstick)## For binary classification, the first factor level is assumed to be the event.
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## compare_models, R2df <- readr::read_csv("diabetes.csv", col_names = TRUE)## Rows: 768 Columns: 9
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## dbl (9): Pregnancies, Glucose, BloodPressure, SkinThickness, Insulin, BMI, D...
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## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.df %>% glimpse()## Rows: 768
## Columns: 9
## $ Pregnancies <dbl> 6, 1, 8, 1, 0, 5, 3, 10, 2, 8, 4, 10, 10, 1, …
## $ Glucose <dbl> 148, 85, 183, 89, 137, 116, 78, 115, 197, 125…
## $ BloodPressure <dbl> 72, 66, 64, 66, 40, 74, 50, 0, 70, 96, 92, 74…
## $ SkinThickness <dbl> 35, 29, 0, 23, 35, 0, 32, 0, 45, 0, 0, 0, 0, …
## $ Insulin <dbl> 0, 0, 0, 94, 168, 0, 88, 0, 543, 0, 0, 0, 0, …
## $ BMI <dbl> 33.6, 26.6, 23.3, 28.1, 43.1, 25.6, 31.0, 35.…
## $ DiabetesPedigreeFunction <dbl> 0.627, 0.351, 0.672, 0.167, 2.288, 0.201, 0.2…
## $ Age <dbl> 50, 31, 32, 21, 33, 30, 26, 29, 53, 54, 30, 3…
## $ Outcome <dbl> 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, …Part 1: Initial analysis of data visualization
1.1 Factor Influence Heat Map
df %>%
cor() %>%
corrplot::corrplot(type = "upper")
According to the heat map we can see that there is a correlation between
the number of pregnancies, body glucose, BMI and age of the
investigators whether they are sick or not.
1.2 Age group proportion
df <- df %>% mutate(Age_Group = cut(df$Age, breaks = c(0, 30, 50, max(df$Age)), labels = c("Under 30", "30-50", "Over 50")))Bar mapping
df %>%
filter(Outcome == 1) %>%
ggplot() +
geom_bar(mapping = aes(x = Age_Group),fill = "steelblue")
Among the investigators, the majority of those with the disease were
concentrated in their 30s and 50s.
df %>% ggplot(mapping = aes(x = Age_Group)) +
geom_bar(aes(fill = as.factor(Outcome)),position = 'fill') +
scale_fill_brewer(name = 'outcome')
Looking at the percentage of patients in that age group reveals that the
percentage of patients aged 30-50 is also the highest.
1.3 Visualize the behavior of the binary outcome with respect to the continuous inputs
df %>%
ggplot(mapping = aes(x = Glucose, y = Outcome))+
geom_point(aes(col = Outcome)) +
geom_smooth(method = 'loess', formula = y ~ x, size = 0.4)+
facet_wrap(~Age_Group, scales = "free")+
theme_bw()## Warning: Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
## ℹ Please use `linewidth` instead.
For both groups below 30 years and above 50 years, the number of
patients increases with higher Glucose.
df %>%
ggplot(mapping = aes(x = Pregnancies, y = Outcome))+
geom_point(aes(col = Outcome)) +
geom_smooth(method = 'loess', formula = y ~ x, size = 0.4)+
facet_wrap(~Age_Group, scales = "free")+
theme_bw()
df %>%
ggplot(mapping = aes(x = BMI, y = Outcome))+
geom_point(aes(col = Outcome)) +
geom_smooth(method = 'loess', formula = y ~ x, size = 0.4)+
facet_wrap(~Age_Group, scales = "free")+
theme_bw()
df %>%
ggplot(mapping = aes(x = Pregnancies + BMI + Glucose, y = Outcome))+
geom_point(aes(col = Outcome)) +
geom_smooth(method = 'loess', formula = y ~ x, size = 0.4)+
facet_wrap(~Age_Group, scales = "free")+
theme_bw()
1.4 Box-line image
df %>% ggplot() +
geom_boxplot(aes(Age, y = Pregnancies),
colour = "blue",
outlier.colour = "red") +
facet_wrap(~Age_Group, scales = "free") +
theme_bw()## Warning: Continuous x aesthetic
## ℹ did you forget `aes(group = ...)`?
df %>% ggplot() +
geom_boxplot(aes(Age, y = BMI),
colour = "blue",
outlier.colour = "red") +
facet_wrap(~Age_Group, scales = "free") +
theme_bw()## Warning: Continuous x aesthetic
## ℹ did you forget `aes(group = ...)`?
Part 2: Modeling analysis
2.1 Divide train set and test set
df <- df %>% mutate(Bloodpress = ifelse(BloodPressure > 0 & BloodPressure < 90,
"Stand",
"Risk"))
df %>% glimpse()## Rows: 768
## Columns: 11
## $ Pregnancies <dbl> 6, 1, 8, 1, 0, 5, 3, 10, 2, 8, 4, 10, 10, 1, …
## $ Glucose <dbl> 148, 85, 183, 89, 137, 116, 78, 115, 197, 125…
## $ BloodPressure <dbl> 72, 66, 64, 66, 40, 74, 50, 0, 70, 96, 92, 74…
## $ SkinThickness <dbl> 35, 29, 0, 23, 35, 0, 32, 0, 45, 0, 0, 0, 0, …
## $ Insulin <dbl> 0, 0, 0, 94, 168, 0, 88, 0, 543, 0, 0, 0, 0, …
## $ BMI <dbl> 33.6, 26.6, 23.3, 28.1, 43.1, 25.6, 31.0, 35.…
## $ DiabetesPedigreeFunction <dbl> 0.627, 0.351, 0.672, 0.167, 2.288, 0.201, 0.2…
## $ Age <dbl> 50, 31, 32, 21, 33, 30, 26, 29, 53, 54, 30, 3…
## $ Outcome <dbl> 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, …
## $ Age_Group <fct> 30-50, 30-50, 30-50, Under 30, 30-50, Under 3…
## $ Bloodpress <chr> "Stand", "Stand", "Stand", "Stand", "Stand", …trainIndex <- sample(1:nrow(df), round(nrow(df)*0.2))
train <- df[trainIndex, ]
test <- df[-trainIndex, ]2.2 Build Model
2.2.1 Categorical variables only – linear additive
mod1_glm <- glm(Outcome ~ Age_Group + Bloodpress , train,family = "binomial")2.2.2 Continuous variables only – linear additive
mod2_glm <- glm(Outcome ~ Pregnancies + Glucose + Insulin + BMI + DiabetesPedigreeFunction, train,family = "binomial")2.2.3 All categorical and continuous variables – linear additive
mod3_glm <- glm(Outcome ~ Pregnancies + Glucose + Insulin + BMI + DiabetesPedigreeFunction + Age_Group + Bloodpress, train,family = "binomial")2.2.4 Interaction of the categorical inputs with all continuous inputs main effects
mod4_glm <- glm(Outcome ~ (Pregnancies + Glucose + Insulin + BMI + DiabetesPedigreeFunction) * (Age_Group + Bloodpress), train,family = "binomial")## Warning: glm.fit: algorithm did not converge## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred2.2.5 Add categorical inputs to all main effect and all pairwise interactions of continuous inputs
mod5_glm <- glm(Outcome ~ (Pregnancies + Glucose + Insulin + BMI + DiabetesPedigreeFunction)^2 + (Age_Group + Bloodpress), data = train,family = "binomial")2.2.6 Interaction of the categorical inputs with all main effect and all pairwise interactions of continuous inputs
mod6_glm <- glm(Outcome ~ (I(Pregnancies)^2 + I(Glucose)^2 + I(Insulin)^2 + I(BMI)^2 + I(DiabetesPedigreeFunction)^2) * (Age_Group + Bloodpress), train,family = "binomial")## Warning: glm.fit: algorithm did not converge## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred2.3 Model Evaluation
2.3.1 R-square
p1 <- broom::glance(mod1_glm)
p2 <- broom::glance(mod2_glm)
p3 <- broom::glance(mod3_glm)
p4 <- broom::glance(mod4_glm)
p5 <- broom::glance(mod5_glm)
p6 <- broom::glance(mod6_glm)
p_all <- rbind(p1,p2,p3,p4,p5,p6) %>%
tibble::rowid_to_column()
p_all## # A tibble: 6 × 9
## rowid null.deviance df.null logLik AIC BIC deviance df.residual nobs
## <int> <dbl> <int> <dbl> <dbl> <dbl> <dbl> <int> <int>
## 1 1 196. 153 -90.7 189. 201. 181. 150 154
## 2 2 196. 153 -78.6 169. 187. 157. 148 154
## 3 3 196. 153 -74.3 167. 194. 149. 145 154
## 4 4 196. 153 -42.7 133. 206. 85.5 130 154
## 5 5 196. 153 -71.1 180. 238. 142. 135 154
## 6 6 196. 153 -42.7 133. 206. 85.5 130 154p_all %>%
ggplot(mapping = aes(x = c(1:6), y = deviance, group = 1))+
geom_path()+
geom_point(size = 2.0)+
theme_bw()
2.3.2 AIC
p_all %>%
ggplot(mapping = aes(x = c(1:6), y = AIC, group = 1)) +
geom_path(color = "red")+
geom_point(size = 2.0)+
theme_bw()
2.3.3 BIC
p_all %>%
ggplot(mapping = aes(x = c(1:6), y = BIC, group = 1))+
geom_path(color = "blue")+
geom_point(size = 2.0)+
theme_bw()
2.4 Prediction
mod1_predict <- predict(mod1_glm, test, type = "response")
mod1_predict_class <- ifelse(mod1_predict > 0.50, 1, 0)
matrix_mod1 <- confusionMatrix(as.factor(mod1_predict_class), as.factor(test$Outcome))
matrix_mod1## Confusion Matrix and Statistics
##
## Reference
## Prediction 0 1
## 0 306 123
## 1 91 94
##
## Accuracy : 0.6515
## 95% CI : (0.6123, 0.6892)
## No Information Rate : 0.6466
## P-Value [Acc > NIR] : 0.41797
##
## Kappa : 0.211
##
## Mcnemar's Test P-Value : 0.03408
##
## Sensitivity : 0.7708
## Specificity : 0.4332
## Pos Pred Value : 0.7133
## Neg Pred Value : 0.5081
## Prevalence : 0.6466
## Detection Rate : 0.4984
## Detection Prevalence : 0.6987
## Balanced Accuracy : 0.6020
##
## 'Positive' Class : 0
## mod2_predict <- predict(mod2_glm, test, type = "response")
mod2_predict_class <- ifelse(mod2_predict > 0.50, 1, 0)
matrix_mod2 <- confusionMatrix(as.factor(mod2_predict_class), as.factor(test$Outcome))
matrix_mod2## Confusion Matrix and Statistics
##
## Reference
## Prediction 0 1
## 0 365 115
## 1 32 102
##
## Accuracy : 0.7606
## 95% CI : (0.7248, 0.7938)
## No Information Rate : 0.6466
## P-Value [Acc > NIR] : 7.399e-10
##
## Kappa : 0.4264
##
## Mcnemar's Test P-Value : 1.349e-11
##
## Sensitivity : 0.9194
## Specificity : 0.4700
## Pos Pred Value : 0.7604
## Neg Pred Value : 0.7612
## Prevalence : 0.6466
## Detection Rate : 0.5945
## Detection Prevalence : 0.7818
## Balanced Accuracy : 0.6947
##
## 'Positive' Class : 0
## mod3_predict <- predict(mod3_glm, test, type = "response")
mod3_predict_class <- ifelse(mod3_predict > 0.50, 1, 0)
matrix_mod3 <- confusionMatrix(as.factor(mod3_predict_class), as.factor(test$Outcome))
matrix_mod3## Confusion Matrix and Statistics
##
## Reference
## Prediction 0 1
## 0 356 104
## 1 41 113
##
## Accuracy : 0.7638
## 95% CI : (0.7282, 0.7969)
## No Information Rate : 0.6466
## P-Value [Acc > NIR] : 2.367e-10
##
## Kappa : 0.4469
##
## Mcnemar's Test P-Value : 2.621e-07
##
## Sensitivity : 0.8967
## Specificity : 0.5207
## Pos Pred Value : 0.7739
## Neg Pred Value : 0.7338
## Prevalence : 0.6466
## Detection Rate : 0.5798
## Detection Prevalence : 0.7492
## Balanced Accuracy : 0.7087
##
## 'Positive' Class : 0
## mod4_predict <- predict(mod4_glm, test, type = "response")
mod4_predict_class <- ifelse(mod4_predict > 0.50, 1, 0)
matrix_mod4 <- confusionMatrix(as.factor(mod4_predict_class), as.factor(test$Outcome))
matrix_mod4## Confusion Matrix and Statistics
##
## Reference
## Prediction 0 1
## 0 313 100
## 1 84 117
##
## Accuracy : 0.7003
## 95% CI : (0.6624, 0.7363)
## No Information Rate : 0.6466
## P-Value [Acc > NIR] : 0.002767
##
## Kappa : 0.3332
##
## Mcnemar's Test P-Value : 0.268807
##
## Sensitivity : 0.7884
## Specificity : 0.5392
## Pos Pred Value : 0.7579
## Neg Pred Value : 0.5821
## Prevalence : 0.6466
## Detection Rate : 0.5098
## Detection Prevalence : 0.6726
## Balanced Accuracy : 0.6638
##
## 'Positive' Class : 0
## mod5_predict <- predict(mod5_glm, test, type = "response")
mod5_predict_class <- ifelse(mod5_predict > 0.50, 1, 0)
matrix_mod5 <- confusionMatrix(as.factor(mod5_predict_class), as.factor(test$Outcome))
matrix_mod5## Confusion Matrix and Statistics
##
## Reference
## Prediction 0 1
## 0 342 101
## 1 55 116
##
## Accuracy : 0.7459
## 95% CI : (0.7095, 0.7799)
## No Information Rate : 0.6466
## P-Value [Acc > NIR] : 8.141e-08
##
## Kappa : 0.416
##
## Mcnemar's Test P-Value : 0.0003147
##
## Sensitivity : 0.8615
## Specificity : 0.5346
## Pos Pred Value : 0.7720
## Neg Pred Value : 0.6784
## Prevalence : 0.6466
## Detection Rate : 0.5570
## Detection Prevalence : 0.7215
## Balanced Accuracy : 0.6980
##
## 'Positive' Class : 0
## mod6_predict <- predict(mod6_glm, test, type = "response")
mod6_predict_class <- ifelse(mod6_predict > 0.50, 1, 0)
matrix_mod6 <- confusionMatrix(as.factor(mod6_predict_class), as.factor(test$Outcome))
matrix_mod6## Confusion Matrix and Statistics
##
## Reference
## Prediction 0 1
## 0 313 100
## 1 84 117
##
## Accuracy : 0.7003
## 95% CI : (0.6624, 0.7363)
## No Information Rate : 0.6466
## P-Value [Acc > NIR] : 0.002767
##
## Kappa : 0.3332
##
## Mcnemar's Test P-Value : 0.268807
##
## Sensitivity : 0.7884
## Specificity : 0.5392
## Pos Pred Value : 0.7579
## Neg Pred Value : 0.5821
## Prevalence : 0.6466
## Detection Rate : 0.5098
## Detection Prevalence : 0.6726
## Balanced Accuracy : 0.6638
##
## 'Positive' Class : 0
## 2.5 Presiction Evaluation
2.5.1 Accuracy
perf_overall <- bind_rows(matrix_mod1$overall,
matrix_mod2$overall,
matrix_mod3$overall,
matrix_mod4$overall,
matrix_mod5$overall,
matrix_mod6$overall
)perf_overall %>%
ggplot(mapping = aes(x = c(1:6), y = Accuracy))+
geom_path()+
geom_point(size = 2.0)
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## ..- attr(*, "class")= chr [1:2] "element_rect" "element"
## $ legend.margin : 'margin' num [1:4] 5.5points 5.5points 5.5points 5.5points
## ..- attr(*, "unit")= int 8
## $ legend.spacing : 'simpleUnit' num 11points
## ..- attr(*, "unit")= int 8
## $ legend.spacing.x : NULL
## $ legend.spacing.y : NULL
## $ legend.key :List of 5
## ..$ fill : chr "white"
## ..$ colour : logi NA
## ..$ linewidth : NULL
## ..$ linetype : NULL
## ..$ inherit.blank: logi TRUE
## ..- attr(*, "class")= chr [1:2] "element_rect" "element"
## $ legend.key.size : 'simpleUnit' num 1.2lines
## ..- attr(*, "unit")= int 3
## $ legend.key.height : NULL
## $ legend.key.width : NULL
## $ legend.text :List of 11
## ..$ family : NULL
## ..$ face : NULL
## ..$ colour : NULL
## ..$ size : 'rel' num 0.8
## ..$ hjust : NULL
## ..$ vjust : NULL
## ..$ angle : NULL
## ..$ lineheight : NULL
## ..$ margin : NULL
## ..$ debug : NULL
## ..$ inherit.blank: logi TRUE
## ..- attr(*, "class")= chr [1:2] "element_text" "element"
## $ legend.text.align : NULL
## $ legend.title :List of 11
## ..$ family : NULL
## ..$ face : NULL
## ..$ colour : NULL
## ..$ size : NULL
## ..$ hjust : num 0
## ..$ vjust : NULL
## ..$ angle : NULL
## ..$ lineheight : NULL
## ..$ margin : NULL
## ..$ debug : NULL
## ..$ inherit.blank: logi TRUE
## ..- attr(*, "class")= chr [1:2] "element_text" "element"
## $ legend.title.align : NULL
## $ legend.position : chr "right"
## $ legend.direction : NULL
## $ legend.justification : chr "center"
## $ legend.box : NULL
## $ legend.box.just : NULL
## $ legend.box.margin : 'margin' num [1:4] 0cm 0cm 0cm 0cm
## ..- attr(*, "unit")= int 1
## $ legend.box.background : list()
## ..- attr(*, "class")= chr [1:2] "element_blank" "element"
## $ legend.box.spacing : 'simpleUnit' num 11points
## ..- attr(*, "unit")= int 8
## $ panel.background :List of 5
## ..$ fill : chr "white"
## ..$ colour : logi NA
## ..$ linewidth : NULL
## ..$ linetype : NULL
## ..$ inherit.blank: logi TRUE
## ..- attr(*, "class")= chr [1:2] "element_rect" "element"
## $ panel.border :List of 5
## ..$ fill : logi NA
## ..$ colour : chr "grey20"
## ..$ linewidth : NULL
## ..$ linetype : NULL
## ..$ inherit.blank: logi TRUE
## ..- attr(*, "class")= chr [1:2] "element_rect" "element"
## $ panel.spacing : 'simpleUnit' num 5.5points
## ..- attr(*, "unit")= int 8
## $ panel.spacing.x : NULL
## $ panel.spacing.y : NULL
## $ panel.grid :List of 6
## ..$ colour : chr "grey92"
## ..$ linewidth : NULL
## ..$ linetype : NULL
## ..$ lineend : NULL
## ..$ arrow : logi FALSE
## ..$ inherit.blank: logi TRUE
## ..- attr(*, "class")= chr [1:2] "element_line" "element"
## $ panel.grid.major : NULL
## $ panel.grid.minor :List of 6
## ..$ colour : NULL
## ..$ linewidth : 'rel' num 0.5
## ..$ linetype : NULL
## ..$ lineend : NULL
## ..$ arrow : logi FALSE
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## ..- attr(*, "class")= chr [1:2] "element_line" "element"
## $ panel.grid.major.x : NULL
## $ panel.grid.major.y : NULL
## $ panel.grid.minor.x : NULL
## $ panel.grid.minor.y : NULL
## $ panel.ontop : logi FALSE
## $ plot.background :List of 5
## ..$ fill : NULL
## ..$ colour : chr "white"
## ..$ linewidth : NULL
## ..$ linetype : NULL
## ..$ inherit.blank: logi TRUE
## ..- attr(*, "class")= chr [1:2] "element_rect" "element"
## $ plot.title :List of 11
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## ..$ face : NULL
## ..$ colour : NULL
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## ..$ vjust : num 1
## ..$ angle : NULL
## ..$ lineheight : NULL
## ..$ margin : 'margin' num [1:4] 0points 0points 5.5points 0points
## .. ..- attr(*, "unit")= int 8
## ..$ debug : NULL
## ..$ inherit.blank: logi TRUE
## ..- attr(*, "class")= chr [1:2] "element_text" "element"
## $ plot.title.position : chr "panel"
## $ plot.subtitle :List of 11
## ..$ family : NULL
## ..$ face : NULL
## ..$ colour : NULL
## ..$ size : NULL
## ..$ hjust : num 0
## ..$ vjust : num 1
## ..$ angle : NULL
## ..$ lineheight : NULL
## ..$ margin : 'margin' num [1:4] 0points 0points 5.5points 0points
## .. ..- attr(*, "unit")= int 8
## ..$ debug : NULL
## ..$ inherit.blank: logi TRUE
## ..- attr(*, "class")= chr [1:2] "element_text" "element"
## $ plot.caption :List of 11
## ..$ family : NULL
## ..$ face : NULL
## ..$ colour : NULL
## ..$ size : 'rel' num 0.8
## ..$ hjust : num 1
## ..$ vjust : num 1
## ..$ angle : NULL
## ..$ lineheight : NULL
## ..$ margin : 'margin' num [1:4] 5.5points 0points 0points 0points
## .. ..- attr(*, "unit")= int 8
## ..$ debug : NULL
## ..$ inherit.blank: logi TRUE
## ..- attr(*, "class")= chr [1:2] "element_text" "element"
## $ plot.caption.position : chr "panel"
## $ plot.tag :List of 11
## ..$ family : NULL
## ..$ face : NULL
## ..$ colour : NULL
## ..$ size : 'rel' num 1.2
## ..$ hjust : num 0.5
## ..$ vjust : num 0.5
## ..$ angle : NULL
## ..$ lineheight : NULL
## ..$ margin : NULL
## ..$ debug : NULL
## ..$ inherit.blank: logi TRUE
## ..- attr(*, "class")= chr [1:2] "element_text" "element"
## $ plot.tag.position : chr "topleft"
## $ plot.margin : 'margin' num [1:4] 5.5points 5.5points 5.5points 5.5points
## ..- attr(*, "unit")= int 8
## $ strip.background :List of 5
## ..$ fill : chr "grey85"
## ..$ colour : chr "grey20"
## ..$ linewidth : NULL
## ..$ linetype : NULL
## ..$ inherit.blank: logi TRUE
## ..- attr(*, "class")= chr [1:2] "element_rect" "element"
## $ strip.background.x : NULL
## $ strip.background.y : NULL
## $ strip.clip : chr "inherit"
## $ strip.placement : chr "inside"
## $ strip.text :List of 11
## ..$ family : NULL
## ..$ face : NULL
## ..$ colour : chr "grey10"
## ..$ size : 'rel' num 0.8
## ..$ hjust : NULL
## ..$ vjust : NULL
## ..$ angle : NULL
## ..$ lineheight : NULL
## ..$ margin : 'margin' num [1:4] 4.4points 4.4points 4.4points 4.4points
## .. ..- attr(*, "unit")= int 8
## ..$ debug : NULL
## ..$ inherit.blank: logi TRUE
## ..- attr(*, "class")= chr [1:2] "element_text" "element"
## $ strip.text.x : NULL
## $ strip.text.y :List of 11
## ..$ family : NULL
## ..$ face : NULL
## ..$ colour : NULL
## ..$ size : NULL
## ..$ hjust : NULL
## ..$ vjust : NULL
## ..$ angle : num -90
## ..$ lineheight : NULL
## ..$ margin : NULL
## ..$ debug : NULL
## ..$ inherit.blank: logi TRUE
## ..- attr(*, "class")= chr [1:2] "element_text" "element"
## $ strip.switch.pad.grid : 'simpleUnit' num 2.75points
## ..- attr(*, "unit")= int 8
## $ strip.switch.pad.wrap : 'simpleUnit' num 2.75points
## ..- attr(*, "unit")= int 8
## $ strip.text.y.left :List of 11
## ..$ family : NULL
## ..$ face : NULL
## ..$ colour : NULL
## ..$ size : NULL
## ..$ hjust : NULL
## ..$ vjust : NULL
## ..$ angle : num 90
## ..$ lineheight : NULL
## ..$ margin : NULL
## ..$ debug : NULL
## ..$ inherit.blank: logi TRUE
## ..- attr(*, "class")= chr [1:2] "element_text" "element"
## - attr(*, "class")= chr [1:2] "theme" "gg"
## - attr(*, "complete")= logi TRUE
## - attr(*, "validate")= logi TRUE2.5.2 Specificity
perf_byClass <- bind_rows(matrix_mod1$byClass,
matrix_mod2$byClass,
matrix_mod3$byClass,
matrix_mod4$byClass,
matrix_mod5$byClass,
matrix_mod6$byClass)perf_byClass %>%
ggplot(mapping = aes(x = c(1:6), y = Specificity))+
geom_path()+
geom_point(size = 2.0)
theme_bw()## List of 94
## $ line :List of 6
## ..$ colour : chr "black"
## ..$ linewidth : num 0.5
## ..$ linetype : num 1
## ..$ lineend : chr "butt"
## ..$ arrow : logi FALSE
## ..$ inherit.blank: logi TRUE
## ..- attr(*, "class")= chr [1:2] "element_line" "element"
## $ rect :List of 5
## ..$ fill : chr "white"
## ..$ colour : chr "black"
## ..$ linewidth : num 0.5
## ..$ linetype : num 1
## ..$ inherit.blank: logi TRUE
## ..- attr(*, "class")= chr [1:2] "element_rect" "element"
## $ text :List of 11
## ..$ family : chr ""
## ..$ face : chr "plain"
## ..$ colour : chr "black"
## ..$ size : num 11
## ..$ hjust : num 0.5
## ..$ vjust : num 0.5
## ..$ angle : num 0
## ..$ lineheight : num 0.9
## ..$ margin : 'margin' num [1:4] 0points 0points 0points 0points
## .. ..- attr(*, "unit")= int 8
## ..$ debug : logi FALSE
## ..$ inherit.blank: logi TRUE
## ..- attr(*, "class")= chr [1:2] "element_text" "element"
## $ title : NULL
## $ aspect.ratio : NULL
## $ axis.title : NULL
## $ axis.title.x :List of 11
## ..$ family : NULL
## ..$ face : NULL
## ..$ colour : NULL
## ..$ size : NULL
## ..$ hjust : NULL
## ..$ vjust : num 1
## ..$ angle : NULL
## ..$ lineheight : NULL
## ..$ margin : 'margin' num [1:4] 2.75points 0points 0points 0points
## .. ..- attr(*, "unit")= int 8
## ..$ debug : NULL
## ..$ inherit.blank: logi TRUE
## ..- attr(*, "class")= chr [1:2] "element_text" "element"
## $ axis.title.x.top :List of 11
## ..$ family : NULL
## ..$ face : NULL
## ..$ colour : NULL
## ..$ size : NULL
## ..$ hjust : NULL
## ..$ vjust : num 0
## ..$ angle : NULL
## ..$ lineheight : NULL
## ..$ margin : 'margin' num [1:4] 0points 0points 2.75points 0points
## .. ..- attr(*, "unit")= int 8
## ..$ debug : NULL
## ..$ inherit.blank: logi TRUE
## ..- attr(*, "class")= chr [1:2] "element_text" "element"
## $ axis.title.x.bottom : NULL
## $ axis.title.y :List of 11
## ..$ family : NULL
## ..$ face : NULL
## ..$ colour : NULL
## ..$ size : NULL
## ..$ hjust : NULL
## ..$ vjust : num 1
## ..$ angle : num 90
## ..$ lineheight : NULL
## ..$ margin : 'margin' num [1:4] 0points 2.75points 0points 0points
## .. ..- attr(*, "unit")= int 8
## ..$ debug : NULL
## ..$ inherit.blank: logi TRUE
## ..- attr(*, "class")= chr [1:2] "element_text" "element"
## $ axis.title.y.left : NULL
## $ axis.title.y.right :List of 11
## ..$ family : NULL
## ..$ face : NULL
## ..$ colour : NULL
## ..$ size : NULL
## ..$ hjust : NULL
## ..$ vjust : num 0
## ..$ angle : num -90
## ..$ lineheight : NULL
## ..$ margin : 'margin' num [1:4] 0points 0points 0points 2.75points
## .. ..- attr(*, "unit")= int 8
## ..$ debug : NULL
## ..$ inherit.blank: logi TRUE
## ..- attr(*, "class")= chr [1:2] "element_text" "element"
## $ axis.text :List of 11
## ..$ family : NULL
## ..$ face : NULL
## ..$ colour : chr "grey30"
## ..$ size : 'rel' num 0.8
## ..$ hjust : NULL
## ..$ vjust : NULL
## ..$ angle : NULL
## ..$ lineheight : NULL
## ..$ margin : NULL
## ..$ debug : NULL
## ..$ inherit.blank: logi TRUE
## ..- attr(*, "class")= chr [1:2] "element_text" "element"
## $ axis.text.x :List of 11
## ..$ family : NULL
## ..$ face : NULL
## ..$ colour : NULL
## ..$ size : NULL
## ..$ hjust : NULL
## ..$ vjust : num 1
## ..$ angle : NULL
## ..$ lineheight : NULL
## ..$ margin : 'margin' num [1:4] 2.2points 0points 0points 0points
## .. ..- attr(*, "unit")= int 8
## ..$ debug : NULL
## ..$ inherit.blank: logi TRUE
## ..- attr(*, "class")= chr [1:2] "element_text" "element"
## $ axis.text.x.top :List of 11
## ..$ family : NULL
## ..$ face : NULL
## ..$ colour : NULL
## ..$ size : NULL
## ..$ hjust : NULL
## ..$ vjust : num 0
## ..$ angle : NULL
## ..$ lineheight : NULL
## ..$ margin : 'margin' num [1:4] 0points 0points 2.2points 0points
## .. ..- attr(*, "unit")= int 8
## ..$ debug : NULL
## ..$ inherit.blank: logi TRUE
## ..- attr(*, "class")= chr [1:2] "element_text" "element"
## $ axis.text.x.bottom : NULL
## $ axis.text.y :List of 11
## ..$ family : NULL
## ..$ face : NULL
## ..$ colour : NULL
## ..$ size : NULL
## ..$ hjust : num 1
## ..$ vjust : NULL
## ..$ angle : NULL
## ..$ lineheight : NULL
## ..$ margin : 'margin' num [1:4] 0points 2.2points 0points 0points
## .. ..- attr(*, "unit")= int 8
## ..$ debug : NULL
## ..$ inherit.blank: logi TRUE
## ..- attr(*, "class")= chr [1:2] "element_text" "element"
## $ axis.text.y.left : NULL
## $ axis.text.y.right :List of 11
## ..$ family : NULL
## ..$ face : NULL
## ..$ colour : NULL
## ..$ size : NULL
## ..$ hjust : num 0
## ..$ vjust : NULL
## ..$ angle : NULL
## ..$ lineheight : NULL
## ..$ margin : 'margin' num [1:4] 0points 0points 0points 2.2points
## .. ..- attr(*, "unit")= int 8
## ..$ debug : NULL
## ..$ inherit.blank: logi TRUE
## ..- attr(*, "class")= chr [1:2] "element_text" "element"
## $ axis.ticks :List of 6
## ..$ colour : chr "grey20"
## ..$ linewidth : NULL
## ..$ linetype : NULL
## ..$ lineend : NULL
## ..$ arrow : logi FALSE
## ..$ inherit.blank: logi TRUE
## ..- attr(*, "class")= chr [1:2] "element_line" "element"
## $ axis.ticks.x : NULL
## $ axis.ticks.x.top : NULL
## $ axis.ticks.x.bottom : NULL
## $ axis.ticks.y : NULL
## $ axis.ticks.y.left : NULL
## $ axis.ticks.y.right : NULL
## $ axis.ticks.length : 'simpleUnit' num 2.75points
## ..- attr(*, "unit")= int 8
## $ axis.ticks.length.x : NULL
## $ axis.ticks.length.x.top : NULL
## $ axis.ticks.length.x.bottom: NULL
## $ axis.ticks.length.y : NULL
## $ axis.ticks.length.y.left : NULL
## $ axis.ticks.length.y.right : NULL
## $ axis.line : list()
## ..- attr(*, "class")= chr [1:2] "element_blank" "element"
## $ axis.line.x : NULL
## $ axis.line.x.top : NULL
## $ axis.line.x.bottom : NULL
## $ axis.line.y : NULL
## $ axis.line.y.left : NULL
## $ axis.line.y.right : NULL
## $ legend.background :List of 5
## ..$ fill : NULL
## ..$ colour : logi NA
## ..$ linewidth : NULL
## ..$ linetype : NULL
## ..$ inherit.blank: logi TRUE
## ..- attr(*, "class")= chr [1:2] "element_rect" "element"
## $ legend.margin : 'margin' num [1:4] 5.5points 5.5points 5.5points 5.5points
## ..- attr(*, "unit")= int 8
## $ legend.spacing : 'simpleUnit' num 11points
## ..- attr(*, "unit")= int 8
## $ legend.spacing.x : NULL
## $ legend.spacing.y : NULL
## $ legend.key :List of 5
## ..$ fill : chr "white"
## ..$ colour : logi NA
## ..$ linewidth : NULL
## ..$ linetype : NULL
## ..$ inherit.blank: logi TRUE
## ..- attr(*, "class")= chr [1:2] "element_rect" "element"
## $ legend.key.size : 'simpleUnit' num 1.2lines
## ..- attr(*, "unit")= int 3
## $ legend.key.height : NULL
## $ legend.key.width : NULL
## $ legend.text :List of 11
## ..$ family : NULL
## ..$ face : NULL
## ..$ colour : NULL
## ..$ size : 'rel' num 0.8
## ..$ hjust : NULL
## ..$ vjust : NULL
## ..$ angle : NULL
## ..$ lineheight : NULL
## ..$ margin : NULL
## ..$ debug : NULL
## ..$ inherit.blank: logi TRUE
## ..- attr(*, "class")= chr [1:2] "element_text" "element"
## $ legend.text.align : NULL
## $ legend.title :List of 11
## ..$ family : NULL
## ..$ face : NULL
## ..$ colour : NULL
## ..$ size : NULL
## ..$ hjust : num 0
## ..$ vjust : NULL
## ..$ angle : NULL
## ..$ lineheight : NULL
## ..$ margin : NULL
## ..$ debug : NULL
## ..$ inherit.blank: logi TRUE
## ..- attr(*, "class")= chr [1:2] "element_text" "element"
## $ legend.title.align : NULL
## $ legend.position : chr "right"
## $ legend.direction : NULL
## $ legend.justification : chr "center"
## $ legend.box : NULL
## $ legend.box.just : NULL
## $ legend.box.margin : 'margin' num [1:4] 0cm 0cm 0cm 0cm
## ..- attr(*, "unit")= int 1
## $ legend.box.background : list()
## ..- attr(*, "class")= chr [1:2] "element_blank" "element"
## $ legend.box.spacing : 'simpleUnit' num 11points
## ..- attr(*, "unit")= int 8
## $ panel.background :List of 5
## ..$ fill : chr "white"
## ..$ colour : logi NA
## ..$ linewidth : NULL
## ..$ linetype : NULL
## ..$ inherit.blank: logi TRUE
## ..- attr(*, "class")= chr [1:2] "element_rect" "element"
## $ panel.border :List of 5
## ..$ fill : logi NA
## ..$ colour : chr "grey20"
## ..$ linewidth : NULL
## ..$ linetype : NULL
## ..$ inherit.blank: logi TRUE
## ..- attr(*, "class")= chr [1:2] "element_rect" "element"
## $ panel.spacing : 'simpleUnit' num 5.5points
## ..- attr(*, "unit")= int 8
## $ panel.spacing.x : NULL
## $ panel.spacing.y : NULL
## $ panel.grid :List of 6
## ..$ colour : chr "grey92"
## ..$ linewidth : NULL
## ..$ linetype : NULL
## ..$ lineend : NULL
## ..$ arrow : logi FALSE
## ..$ inherit.blank: logi TRUE
## ..- attr(*, "class")= chr [1:2] "element_line" "element"
## $ panel.grid.major : NULL
## $ panel.grid.minor :List of 6
## ..$ colour : NULL
## ..$ linewidth : 'rel' num 0.5
## ..$ linetype : NULL
## ..$ lineend : NULL
## ..$ arrow : logi FALSE
## ..$ inherit.blank: logi TRUE
## ..- attr(*, "class")= chr [1:2] "element_line" "element"
## $ panel.grid.major.x : NULL
## $ panel.grid.major.y : NULL
## $ panel.grid.minor.x : NULL
## $ panel.grid.minor.y : NULL
## $ panel.ontop : logi FALSE
## $ plot.background :List of 5
## ..$ fill : NULL
## ..$ colour : chr "white"
## ..$ linewidth : NULL
## ..$ linetype : NULL
## ..$ inherit.blank: logi TRUE
## ..- attr(*, "class")= chr [1:2] "element_rect" "element"
## $ plot.title :List of 11
## ..$ family : NULL
## ..$ face : NULL
## ..$ colour : NULL
## ..$ size : 'rel' num 1.2
## ..$ hjust : num 0
## ..$ vjust : num 1
## ..$ angle : NULL
## ..$ lineheight : NULL
## ..$ margin : 'margin' num [1:4] 0points 0points 5.5points 0points
## .. ..- attr(*, "unit")= int 8
## ..$ debug : NULL
## ..$ inherit.blank: logi TRUE
## ..- attr(*, "class")= chr [1:2] "element_text" "element"
## $ plot.title.position : chr "panel"
## $ plot.subtitle :List of 11
## ..$ family : NULL
## ..$ face : NULL
## ..$ colour : NULL
## ..$ size : NULL
## ..$ hjust : num 0
## ..$ vjust : num 1
## ..$ angle : NULL
## ..$ lineheight : NULL
## ..$ margin : 'margin' num [1:4] 0points 0points 5.5points 0points
## .. ..- attr(*, "unit")= int 8
## ..$ debug : NULL
## ..$ inherit.blank: logi TRUE
## ..- attr(*, "class")= chr [1:2] "element_text" "element"
## $ plot.caption :List of 11
## ..$ family : NULL
## ..$ face : NULL
## ..$ colour : NULL
## ..$ size : 'rel' num 0.8
## ..$ hjust : num 1
## ..$ vjust : num 1
## ..$ angle : NULL
## ..$ lineheight : NULL
## ..$ margin : 'margin' num [1:4] 5.5points 0points 0points 0points
## .. ..- attr(*, "unit")= int 8
## ..$ debug : NULL
## ..$ inherit.blank: logi TRUE
## ..- attr(*, "class")= chr [1:2] "element_text" "element"
## $ plot.caption.position : chr "panel"
## $ plot.tag :List of 11
## ..$ family : NULL
## ..$ face : NULL
## ..$ colour : NULL
## ..$ size : 'rel' num 1.2
## ..$ hjust : num 0.5
## ..$ vjust : num 0.5
## ..$ angle : NULL
## ..$ lineheight : NULL
## ..$ margin : NULL
## ..$ debug : NULL
## ..$ inherit.blank: logi TRUE
## ..- attr(*, "class")= chr [1:2] "element_text" "element"
## $ plot.tag.position : chr "topleft"
## $ plot.margin : 'margin' num [1:4] 5.5points 5.5points 5.5points 5.5points
## ..- attr(*, "unit")= int 8
## $ strip.background :List of 5
## ..$ fill : chr "grey85"
## ..$ colour : chr "grey20"
## ..$ linewidth : NULL
## ..$ linetype : NULL
## ..$ inherit.blank: logi TRUE
## ..- attr(*, "class")= chr [1:2] "element_rect" "element"
## $ strip.background.x : NULL
## $ strip.background.y : NULL
## $ strip.clip : chr "inherit"
## $ strip.placement : chr "inside"
## $ strip.text :List of 11
## ..$ family : NULL
## ..$ face : NULL
## ..$ colour : chr "grey10"
## ..$ size : 'rel' num 0.8
## ..$ hjust : NULL
## ..$ vjust : NULL
## ..$ angle : NULL
## ..$ lineheight : NULL
## ..$ margin : 'margin' num [1:4] 4.4points 4.4points 4.4points 4.4points
## .. ..- attr(*, "unit")= int 8
## ..$ debug : NULL
## ..$ inherit.blank: logi TRUE
## ..- attr(*, "class")= chr [1:2] "element_text" "element"
## $ strip.text.x : NULL
## $ strip.text.y :List of 11
## ..$ family : NULL
## ..$ face : NULL
## ..$ colour : NULL
## ..$ size : NULL
## ..$ hjust : NULL
## ..$ vjust : NULL
## ..$ angle : num -90
## ..$ lineheight : NULL
## ..$ margin : NULL
## ..$ debug : NULL
## ..$ inherit.blank: logi TRUE
## ..- attr(*, "class")= chr [1:2] "element_text" "element"
## $ strip.switch.pad.grid : 'simpleUnit' num 2.75points
## ..- attr(*, "unit")= int 8
## $ strip.switch.pad.wrap : 'simpleUnit' num 2.75points
## ..- attr(*, "unit")= int 8
## $ strip.text.y.left :List of 11
## ..$ family : NULL
## ..$ face : NULL
## ..$ colour : NULL
## ..$ size : NULL
## ..$ hjust : NULL
## ..$ vjust : NULL
## ..$ angle : num 90
## ..$ lineheight : NULL
## ..$ margin : NULL
## ..$ debug : NULL
## ..$ inherit.blank: logi TRUE
## ..- attr(*, "class")= chr [1:2] "element_text" "element"
## - attr(*, "class")= chr [1:2] "theme" "gg"
## - attr(*, "complete")= logi TRUE
## - attr(*, "validate")= logi TRUE2.5.3 Sensitivity
perf_byClass %>%
ggplot(mapping = aes(x = c(1:6), y = Sensitivity))+
geom_path()+
geom_point(size = 2.0)
theme_bw()## List of 94
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## - attr(*, "validate")= logi TRUE2.5.4 Precision
perf_byClass %>%
ggplot(mapping = aes(x = c(1:6), y = Precision))+
geom_path()+
geom_point(size = 2.0)
theme_bw()## List of 94
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## - attr(*, "validate")= logi TRUEAccording to all analysis, model 2 and model 3 are the best and the second best model. Because they have low AIC and BIC, and also have high precision, sensitivity and Accurancy. Although model 3 Specificity is not very good, but I think overall he is still a model worth continuing to try to conduct analysis.
2.6 Presiction Evaluation
2.6.1 Model 2
mod2_glm %>%
coefplot(scales = "free", sort = "natural", pointSize = 1, innerCI = 0.5)+
geom_vline(xintercept = 0, color = "red")+
theme_bw()+
theme(legend.position = 'none')
import_mod2 <- mod2_glm %>%
coefplot(sort = "magnitude", plot = FALSE) %>%
tibble::as_tibble() %>%
filter((HighOuter > 0 & LowOuter > 0) | (HighOuter < 0 & LowOuter < 0))
import_mod2## # A tibble: 3 × 7
## Value Coefficient HighInner LowInner HighOuter LowOuter Model
## <dbl> <fct> <dbl> <dbl> <dbl> <dbl> <chr>
## 1 -6.55 (Intercept) -5.30 -7.80 -4.05 -9.05 model
## 2 0.0209 Glucose 0.0274 0.0143 0.0340 0.00781 model
## 3 0.0724 BMI 0.103 0.0416 0.134 0.0107 modelThere are 4 significant coefficient features in model 2 and Glucose is the most important.
2.6.2 Model 3
mod3_glm %>%
coefplot(scales = "free", sort = "natural", pointSize = 1, innerCI = 0.5)+
geom_vline(xintercept = 0, color = "red")+
theme_bw()+
theme(legend.position = 'none')
import_mod3 <- mod3_glm %>%
coefplot(sort = "magnitude", plot = FALSE) %>%
tibble::as_tibble() %>%
filter((HighOuter > 0 & LowOuter > 0) | (HighOuter < 0 & LowOuter < 0))
import_mod3## # A tibble: 4 × 7
## Value Coefficient HighInner LowInner HighOuter LowOuter Model
## <dbl> <fct> <dbl> <dbl> <dbl> <dbl> <chr>
## 1 -6.86 (Intercept) -5.35 -8.37 -3.84 -9.89 model
## 2 0.0208 Glucose 0.0276 0.0141 0.0343 0.00737 model
## 3 0.0693 BMI 0.102 0.0368 0.134 0.00419 model
## 4 1.68 Age_Group30-50 2.26 1.09 2.85 0.505 modelPart 3 Model compare and selection
3.1 Fit Model
3.1.1 Model 2
class_stan_glm_mod2 <- stan_glm(formula(mod2_glm),
data = df,
family = binomial(link = "logit"),
prior_intercept = NULL,
refresh = 0,
seed = 123123,
chains = 1,
iter = 300)## Warning: The largest R-hat is 1.05, indicating chains have not mixed.
## Running the chains for more iterations may help. See
## https://mc-stan.org/misc/warnings.html#r-hat## Warning: Bulk Effective Samples Size (ESS) is too low, indicating posterior means and medians may be unreliable.
## Running the chains for more iterations may help. See
## https://mc-stan.org/misc/warnings.html#bulk-ess## Warning: Tail Effective Samples Size (ESS) is too low, indicating posterior variances and tail quantiles may be unreliable.
## Running the chains for more iterations may help. See
## https://mc-stan.org/misc/warnings.html#tail-ess3.1.2 Model 3
class_stan_glm_mod3 <- stan_glm(formula(mod3_glm),
data = df,
family = binomial(link = "logit"),
prior_intercept = NULL,
refresh = 0,
seed = 123123,
chains = 1,
iter = 300)## Warning: Tail Effective Samples Size (ESS) is too low, indicating posterior variances and tail quantiles may be unreliable.
## Running the chains for more iterations may help. See
## https://mc-stan.org/misc/warnings.html#tail-ess3.2 WAIC compare
class_stan_glm_mod2$waic <- waic(class_stan_glm_mod2)## Warning:
## 1 (0.1%) p_waic estimates greater than 0.4. We recommend trying loo instead.class_stan_glm_mod3$waic <- waic(class_stan_glm_mod3)## Warning:
## 1 (0.1%) p_waic estimates greater than 0.4. We recommend trying loo instead.loo_class_stan_glm_mod2 <- loo(class_stan_glm_mod2)
loo_class_stan_glm_mod3 <- loo(class_stan_glm_mod3)plot(loo_class_stan_glm_mod2, label_points = TRUE)
plot(loo_class_stan_glm_mod3, label_points = TRUE)
loo_compare(loo_class_stan_glm_mod2, loo_class_stan_glm_mod3)## elpd_diff se_diff
## class_stan_glm_mod3 0.0 0.0
## class_stan_glm_mod2 -4.2 4.1According to the WAIC compare, I think the model 3 is the best model.
Part 4 Train/tune with resampling
4.1 Accuracy - AUC
4.1.1 Train parameter
my_ctrl_acc <- trainControl(method = "repeatedcv",
number = 5,
repeats = 3,
savePredictions = TRUE)
my_metric_acc <- "Accuracy"4.1.2 Build Model
All categorical and continuous inputs - linear additive features
df_4 <- df %>% subset(select = c(Pregnancies, Glucose, Insulin,
BMI, DiabetesPedigreeFunction, Age_Group,
Bloodpress)) %>%
mutate(outcome = ifelse(df$Outcome == 1,
"event",
"non_event"))set.seed(1234)
acc_glm_add <- train(outcome ~ .,
data = df_4,
method = "glm",
metric = my_metric_acc,
preProcess = c("center", "scale"),
trControl = my_ctrl_acc)
acc_glm_add## Generalized Linear Model
##
## 768 samples
## 7 predictor
## 2 classes: 'event', 'non_event'
##
## Pre-processing: centered (8), scaled (8)
## Resampling: Cross-Validated (5 fold, repeated 3 times)
## Summary of sample sizes: 614, 615, 614, 614, 615, 615, ...
## Resampling results:
##
## Accuracy Kappa
## 0.7677758 0.46407294.1.3 Regularized regression with Elastic net
set.seed(1234)
acc_glm_enet_pair <- train(outcome ~ .,
data = df_4,
method = "glmnet",
metric = my_metric_acc,
preProcess = c("center", "scale"),
trControl = my_ctrl_acc)
acc_glm_enet_pair## glmnet
##
## 768 samples
## 7 predictor
## 2 classes: 'event', 'non_event'
##
## Pre-processing: centered (8), scaled (8)
## Resampling: Cross-Validated (5 fold, repeated 3 times)
## Summary of sample sizes: 614, 615, 614, 614, 615, 615, ...
## Resampling results across tuning parameters:
##
## alpha lambda Accuracy Kappa
## 0.10 0.0004447834 0.7686416 0.4651583
## 0.10 0.0044478343 0.7703817 0.4687834
## 0.10 0.0444783425 0.7751464 0.4720382
## 0.55 0.0004447834 0.7686416 0.4651610
## 0.55 0.0044478343 0.7708146 0.4696151
## 0.55 0.0444783425 0.7734007 0.4619488
## 1.00 0.0004447834 0.7682087 0.4643187
## 1.00 0.0044478343 0.7695074 0.4666635
## 1.00 0.0444783425 0.7682087 0.4466208
##
## Accuracy was used to select the optimal model using the largest value.
## The final values used for the model were alpha = 0.1 and lambda = 0.04447834.4.1.4 Neural network
set.seed(1234)
acc_nnet_warmup <- train(outcome ~ .,
data = df_4,
method = "nnet",
metric = my_metric_acc,
preProcess = c("center", "scale"),
trControl = my_ctrl_acc,
trace = FALSE)plot(acc_nnet_warmup, xTrans = log)
Tune
tune_grid_neural <- expand.grid(size = c(3, 5, 10, 15, 20),
decay = exp(seq(-9, 0, length.out = 11)))
acc_nnet_tune <- train(outcome ~ .,
data = df_4,
method = "nnet",
metric = my_metric_acc,
tuneGrid = tune_grid_neural,
preProcess = c("center", "scale"),
trControl = my_ctrl_acc,
trace = FALSE)
plot(acc_nnet_tune, xTrans = log)
4.1.5 Random forest
set.seed(1234)
acc_rf_warmup <- train(outcome ~ .,
data = df_4,
method = "rf",
metric = my_metric_acc,
preProcess = c("center", "scale"),
trControl = my_ctrl_acc,
trace = FALSE)plot(acc_rf_warmup, xTrans = log)
Tune
set.seed(1234)
acc_rf_tune <- train(outcome ~ .,
data = df_4,
method = "rf",
metric = my_metric_acc,
trControl = my_ctrl_acc,
tuneGrid = expand.grid(mtry = seq(2, 8, by = 1)),
importance = TRUE)plot(acc_rf_tune, xTrans = log)
4.1.6 Gradient boosted tree
set.seed(1234)
acc_gbm_warmup <- train(outcome ~ .,
data = df_4,
method = "gbm",
metric = my_metric_acc,
trControl = my_ctrl_acc,
verbose = FALSE)
plot(acc_gbm_warmup)
Tune
acc_gbm_grid <- expand.grid(n.trees = c(100, 150, 300, 500, 750, 1000),
shrinkage = c(0.01, 0.1),
interaction.depth = acc_gbm_warmup$bestTune$interaction.depth,
n.minobsinnode = acc_gbm_warmup$bestTune$n.minobsinnode)set.seed(1234)
acc_gbm_tune <- train(outcome ~ .,
data = df_4,
method = "gbm",
metric = my_metric_acc,
tuneGrid = acc_gbm_grid,
trControl = my_ctrl_acc,
verbose=FALSE)
plot(acc_gbm_tune)
4.1.7 SVM
set.seed(1234)
acc_svm_warmup <- train(outcome ~ .,
data = df_4,
method = "svmRadial",
metric = my_metric_acc,
preProcess = c("center", "scale"),
trControl = my_ctrl_acc)
plot(acc_svm_warmup)
Tune
svm_grid <- expand.grid(sigma = seq(0.01, 1, length = 10),
C = 2^(-5:5))set.seed(1234)
acc_svm_tuned <- train(outcome ~ .,
data = df_4,
method = "svmRadial",
metric = my_metric_acc,
tuneGrid = svm_grid,
preProcess = c("center", "scale"),
trControl = my_ctrl_acc)
plot(acc_svm_tuned)
4.2 ROC
4.2.1 Train parameter
my_ctrl <- trainControl(method = "repeatedcv",
number = 5,
repeats = 3,
summaryFunction = twoClassSummary,
classProbs = TRUE,
savePredictions = TRUE)
my_metric <- "ROC"4.2.2 Build model
set.seed(1234)
roc_glm_add <- train(outcome ~ .,
data = df_4,
method = "glm",
metric = my_metric,
preProcess = c("center", "scale"),
trControl = my_ctrl)
roc_glm_add## Generalized Linear Model
##
## 768 samples
## 7 predictor
## 2 classes: 'event', 'non_event'
##
## Pre-processing: centered (8), scaled (8)
## Resampling: Cross-Validated (5 fold, repeated 3 times)
## Summary of sample sizes: 614, 615, 614, 614, 615, 615, ...
## Resampling results:
##
## ROC Sens Spec
## 0.8353038 0.5659679 0.8764.2.3 Regularized regression with Elastic net
set.seed(1234)
roc_glm_enet <- train(outcome ~ .,
data = df_4,
method = "glmnet",
metric = my_metric,
preProcess = c("center", "scale"),
trControl = my_ctrl)
roc_glm_enet## glmnet
##
## 768 samples
## 7 predictor
## 2 classes: 'event', 'non_event'
##
## Pre-processing: centered (8), scaled (8)
## Resampling: Cross-Validated (5 fold, repeated 3 times)
## Summary of sample sizes: 614, 615, 614, 614, 615, 615, ...
## Resampling results across tuning parameters:
##
## alpha lambda ROC Sens Spec
## 0.10 0.0004447834 0.8354041 0.5634754 0.8786667
## 0.10 0.0044478343 0.8356622 0.5647333 0.8806667
## 0.10 0.0444783425 0.8358444 0.5422781 0.9000000
## 0.55 0.0004447834 0.8354743 0.5634754 0.8786667
## 0.55 0.0044478343 0.8356834 0.5647100 0.8813333
## 0.55 0.0444783425 0.8346997 0.5161426 0.9113333
## 1.00 0.0004447834 0.8354493 0.5634754 0.8780000
## 1.00 0.0044478343 0.8355197 0.5634521 0.8800000
## 1.00 0.0444783425 0.8290256 0.4975775 0.9133333
##
## ROC was used to select the optimal model using the largest value.
## The final values used for the model were alpha = 0.1 and lambda = 0.04447834.4.2.4 Neural network
set.seed(1234)
roc_nnet_warmup <- train(outcome ~ .,
data = df_4,
method = "nnet",
metric = my_metric,
preProcess = c("center", "scale"),
trControl = my_ctrl,
trace = FALSE)plot(roc_nnet_warmup, xTrans = log)
Tune
roc_nnet_tune <- train(outcome ~ .,
data = df_4,
method = "nnet",
metric = my_metric,
tuneGrid = tune_grid_neural,
preProcess = c("center", "scale"),
trControl = my_ctrl,
trace = FALSE)
plot(roc_nnet_tune, xTrans = log)
4.2.5 Random forest
set.seed(1234)
roc_rf_warmup <- train(outcome ~ .,
data = df_4,
method = "rf",
metric = my_metric,
preProcess = c("center", "scale"),
trControl = my_ctrl,
trace = FALSE)plot(roc_rf_warmup, xTrans = log)
Tune
set.seed(1234)
roc_rf_tune <- train(outcome ~ .,
data = df_4,
method = "rf",
metric = my_metric,
trControl = my_ctrl,
tuneGrid = expand.grid(mtry = seq(2, 8, by = 1)),
importance = TRUE)plot(roc_rf_tune, xTrans = log)
4.2.6 Gradient boosted tree
set.seed(1234)
roc_gbm_warmup <- train(outcome ~ .,
data = df_4,
method = "gbm",
metric = my_metric,
trControl = my_ctrl,
verbose = FALSE)
plot(roc_gbm_warmup)
Tune
roc_gbm_grid <- expand.grid(n.trees = c(100, 150, 300, 500, 750, 1000),
shrinkage = c(0.01, 0.1),
interaction.depth = roc_gbm_warmup$bestTune$interaction.depth,
n.minobsinnode = roc_gbm_warmup$bestTune$n.minobsinnode)set.seed(1234)
roc_gbm_tune <- train(outcome ~ .,
data = df_4,
method = "gbm",
metric = my_metric,
tuneGrid = roc_gbm_grid,
trControl = my_ctrl,
verbose=FALSE)
plot(roc_gbm_tune)
4.2.7 SVM
set.seed(1234)
roc_svm_warmup <- train(outcome ~ .,
data = df_4,
method = "svmRadial",
metric = my_metric,
preProcess = c("center", "scale"),
trControl = my_ctrl)
plot(roc_svm_warmup)
Tune
set.seed(1234)
roc_svm_tuned <- train(outcome ~ .,
data = df_4,
method = "svmRadial",
metric = my_metric,
tuneGrid = svm_grid,
preProcess = c("center", "scale"),
trControl = my_ctrl)
plot(roc_svm_tuned)
4.3 Identify the best model.
4.3.1 Accurancy
ACC_perform <- resamples(list(ACC_GLM_ADD = acc_glm_add,
ENET_PAIR = acc_glm_enet_pair,
GBM_WARMUP = acc_gbm_warmup,
GBM_TUNE = acc_gbm_tune,
NNET_WARMUP = acc_nnet_warmup,
NNET_TUNE = acc_nnet_tune,
RF_WARMUP = acc_rf_warmup,
RF_TUNE = acc_rf_tune,
SVM_WARMUOP = acc_svm_warmup,
SVM_TUNE = acc_svm_tuned
)
)dotplot(ACC_perform, metric = "Accuracy")
According to the Accuracy result, NNet tuned model is the best.
4.3.2 ROC
ROC_perform <- resamples(list(ACC_GLM_ADD = roc_glm_add,
ENET_PAIR = roc_glm_enet,
GBM_WARMUP = roc_gbm_warmup,
GBM_TUNE = roc_gbm_tune,
NNET_WARMUP = roc_nnet_warmup,
NNET_TUNE = roc_nnet_tune,
RF_WARMUP = roc_rf_warmup,
RF_TUNE = roc_rf_tune,
SVM_WARMUOP = roc_svm_warmup,
SVM_TUNE = roc_svm_tuned
)
)dotplot(ROC_perform, metric = "ROC")
According to the ROC, the best model is the SVM tuned model.
5. Final analysis
5.1 Find the important feature in two model
I choose the NNet to do the final analysis #### NNet tuned model
library(NeuralNetTools)
olden(acc_nnet_tune$finalModel)
5.2 Train best model and draw ROC curve
trainIndex_new <- sample(1:nrow(df_4), round(nrow(df_4)*0.2))
train_new <- df_4[trainIndex_new, ]
test_new <- df_4[-trainIndex_new, ]acc_nnet_tune_train <- train(outcome ~ .,
data = train_new,
method = "nnet",
metric = my_metric_acc,
tuneGrid = tune_grid_neural,
preProcess = c("center", "scale"),
trControl = my_ctrl_acc,
trace = FALSE)library(pROC)## Type 'citation("pROC")' for a citation.##
## Attaching package: 'pROC'## The following objects are masked from 'package:stats':
##
## cov, smooth, vargrid_pred <- predict(acc_nnet_tune_train, test_new, type = "prob")
grid_pred %>% glimpse()## Rows: 614
## Columns: 2
## $ event <dbl> 0.62340196, 0.14460341, 0.69417969, 0.09287587, 0.16691780, …
## $ non_event <dbl> 0.3765980, 0.8553966, 0.3058203, 0.9071241, 0.8330822, 0.907…grid_roc <- roc(test_new$outcome, grid_pred[,1])## Setting levels: control = event, case = non_event## Setting direction: controls > casesplot.roc(grid_roc)
Total_count <- grid_roc$sensitivities + grid_roc$specificities
Best_Threshold <- which(Total_count == max(Total_count))
Best_cutoff <- grid_roc$thresholds[Best_Threshold]
Best_cutoff## [1] 0.3225715